CGAL 5.0 - Polygon Mesh Processing
Geometric Measure Functions

Functions to compute lengths of edges and borders, areas of faces and patches, as well as volumes of closed meshes.

## Functions

template<typename PolygonMesh , typename NamedParameters >
FT CGAL::Polygon_mesh_processing::edge_length (typename boost::graph_traits< PolygonMesh >::halfedge_descriptor h, const PolygonMesh &pmesh, const NamedParameters &np)
computes the length of an edge of a given polygon mesh. More...

template<typename PolygonMesh , typename NamedParameters >
FT CGAL::Polygon_mesh_processing::face_border_length (typename boost::graph_traits< PolygonMesh >::halfedge_descriptor h, const PolygonMesh &pmesh, const NamedParameters &np)
computes the length of the border polyline that contains a given halfedge. More...

template<typename PolygonMesh , typename NamedParameters >
std::pair< halfedge_descriptor, FT > CGAL::Polygon_mesh_processing::longest_border (const PolygonMesh &pmesh, const NamedParameters &np)
finds the longest border of a given triangulated surface and returns a halfedge that is part of this border and the length of this border. More...

template<typename TriangleMesh , typename NamedParameters >
FT CGAL::Polygon_mesh_processing::face_area (typename boost::graph_traits< TriangleMesh >::face_descriptor f, const TriangleMesh &tmesh, const NamedParameters &np)
computes the area of a face of a given triangulated surface mesh. More...

template<typename FaceRange , typename TriangleMesh , typename NamedParameters >
FT CGAL::Polygon_mesh_processing::area (FaceRange face_range, const TriangleMesh &tmesh, const NamedParameters &np)
computes the area of a range of faces of a given triangulated surface mesh. More...

template<typename TriangleMesh , typename NamedParameters >
FT CGAL::Polygon_mesh_processing::area (const TriangleMesh &tmesh, const NamedParameters &np)
computes the surface area of a triangulated surface mesh. More...

template<typename TriangleMesh , typename NamedParameters >
FT CGAL::Polygon_mesh_processing::volume (const TriangleMesh &tmesh, const NamedParameters &np)
computes the volume of the domain bounded by a closed triangulated surface mesh. More...

template<typename TriangleMesh , typename NamedParameters >
FT CGAL::Polygon_mesh_processing::face_aspect_ratio (typename boost::graph_traits< TriangleMesh >::face_descriptor f, const TriangleMesh &tmesh, const NamedParameters &np)
computes the aspect ratio of a face of a given triangulated surface mesh. More...

template<typename TriangleMesh , typename NamedParameters >
Point_3 CGAL::Polygon_mesh_processing::centroid (const TriangleMesh &tmesh, const NamedParameters &np)
computes the centroid of a volume bounded by a closed triangulated surface mesh. More...

## ◆ area() [1/2]

template<typename FaceRange , typename TriangleMesh , typename NamedParameters >
 FT CGAL::Polygon_mesh_processing::area ( FaceRange face_range, const TriangleMesh & tmesh, const NamedParameters & np )

#include <CGAL/Polygon_mesh_processing/measure.h>

computes the area of a range of faces of a given triangulated surface mesh.

Template Parameters
 FaceRange range of boost::graph_traits::face_descriptor, model of Range. Its iterator type is InputIterator. TriangleMesh a model of HalfedgeGraph NamedParameters a sequence of Named Parameters
Parameters
 face_range the range of faces of which the area is computed tmesh the triangulated surface mesh to which the faces of face_range belong np optional sequence of Named Parameters among the ones listed below
Named Parameters
 vertex_point_map the property map with the points associated to the vertices of pmesh. If this parameter is omitted, an internal property map for CGAL::vertex_point_t must be available in TriangleMesh geom_traits an instance of a geometric traits class, model of Kernel
Returns
sum of face areas of faces. The return type FT is a number type. It is either deduced from the geom_traits Named Parameters if provided, or the geometric traits class deduced from the point property map of tmesh.
Warning
This function involves a square root computation. If Kernel::FT does not have a sqrt() operation, the square root computation will be done approximately.
face_area()

## ◆ area() [2/2]

template<typename TriangleMesh , typename NamedParameters >
 FT CGAL::Polygon_mesh_processing::area ( const TriangleMesh & tmesh, const NamedParameters & np )

#include <CGAL/Polygon_mesh_processing/measure.h>

computes the surface area of a triangulated surface mesh.

Template Parameters
 TriangleMesh a model of HalfedgeGraph NamedParameters a sequence of Named Parameters
Parameters
 tmesh the triangulated surface mesh np optional sequence of Named Parameters among the ones listed below
Named Parameters
 vertex_point_map the property map with the points associated to the vertices of pmesh. If this parameter is omitted, an internal property map for CGAL::vertex_point_t must be available in TriangleMesh geom_traits an instance of a geometric traits class, model of Kernel
Returns
the surface area of tmesh. The return type FT is a number type. It is either deduced from the geom_traits Named Parameters if provided, or the geometric traits class deduced from the point property map of tmesh.
Warning
This function involves a square root computation. If Kernel::FT does not have a sqrt() operation, the square root computation will be done approximately.
face_area()

## ◆ centroid()

template<typename TriangleMesh , typename NamedParameters >
 Point_3 CGAL::Polygon_mesh_processing::centroid ( const TriangleMesh & tmesh, const NamedParameters & np )

#include <CGAL/Polygon_mesh_processing/measure.h>

computes the centroid of a volume bounded by a closed triangulated surface mesh.

Template Parameters
 TriangleMesh a model of FaceListGraph NamedParameters a sequence of Named Parameters
Parameters
 tmesh the closed triangulated surface mesh bounding the volume np optional sequence of Named Parameters among the ones listed below
Precondition
tmesh is closed
Named Parameters
 vertex_point_map the property map with the points associated to the vertices of pmesh. If this parameter is omitted, an internal property map for CGAL::vertex_point_t must be available in TriangleMesh geom_traits an instance of a geometric traits class, model of Kernel
Returns
the centroid of the domain bounded by tmesh.

## ◆ edge_length()

template<typename PolygonMesh , typename NamedParameters >
 FT CGAL::Polygon_mesh_processing::edge_length ( typename boost::graph_traits< PolygonMesh >::halfedge_descriptor h, const PolygonMesh & pmesh, const NamedParameters & np )

#include <CGAL/Polygon_mesh_processing/measure.h>

computes the length of an edge of a given polygon mesh.

The edge is given by one of its halfedges, or the edge itself.

Template Parameters
 PolygonMesh a model of HalfedgeGraph NamedParameters a sequence of Named Parameters
Parameters
 h one halfedge of the edge to compute the length pmesh the polygon mesh to which h belongs np optional sequence of Named Parameters among the ones listed below
Named Parameters
 vertex_point_map the property map with the points associated to the vertices of pmesh. If this parameter is omitted, an internal property map for CGAL::vertex_point_t must be available in PolygonMesh geom_traits an instance of a geometric traits class, model of Kernel
Returns
the length of h. The return type FT is a number type. It is either deduced from the geom_traits Named Parameters if provided, or the geometric traits class deduced from the point property map of pmesh.
Warning
This function involves a square root computation. If FT does not have a sqrt() operation, the square root computation will be done approximately.
face_border_length()

## ◆ face_area()

template<typename TriangleMesh , typename NamedParameters >
 FT CGAL::Polygon_mesh_processing::face_area ( typename boost::graph_traits< TriangleMesh >::face_descriptor f, const TriangleMesh & tmesh, const NamedParameters & np )

#include <CGAL/Polygon_mesh_processing/measure.h>

computes the area of a face of a given triangulated surface mesh.

Template Parameters
 TriangleMesh a model of HalfedgeGraph NamedParameters a sequence of Named Parameters
Parameters
 f the face of which the area is computed tmesh the triangulated surface mesh to which f belongs np optional sequence of Named Parameters among the ones listed below
Named Parameters
 vertex_point_map the property map with the points associated to the vertices of pmesh. If this parameter is omitted, an internal property map for CGAL::vertex_point_t must be available in TriangleMesh geom_traits an instance of a geometric traits class, model of Kernel
Precondition
f != boost::graph_traits<TriangleMesh>::null_face()
Returns
the area of f. The return type FT is a number type. It is either deduced from the geom_traits Named Parameters if provided, or the geometric traits class deduced from the point property map of tmesh.
area()

## ◆ face_aspect_ratio()

template<typename TriangleMesh , typename NamedParameters >
 FT CGAL::Polygon_mesh_processing::face_aspect_ratio ( typename boost::graph_traits< TriangleMesh >::face_descriptor f, const TriangleMesh & tmesh, const NamedParameters & np )

#include <CGAL/Polygon_mesh_processing/measure.h>

computes the aspect ratio of a face of a given triangulated surface mesh.

Template Parameters
 TriangleMesh a model of HalfedgeGraph NamedParameters a sequence of Named Parameters
Parameters
 f the face of which the aspect ratio is computed tmesh the triangulated surface mesh to which f belongs np optional sequence of Named Parameters among the ones listed below
Named Parameters
 vertex_point_map the property map with the points associated to the vertices of pmesh. If this parameter is omitted, an internal property map for CGAL::vertex_point_t must be available in TriangleMesh geom_traits an instance of a geometric traits class, model of Kernel
Precondition
f != boost::graph_traits<TriangleMesh>::null_face()
Returns
the aspect ratio of f. The return type FT is a number type. It is either deduced from the geom_traits Named Parameters if provided, or the geometric traits class deduced from the point property map of tmesh.

## ◆ face_border_length()

template<typename PolygonMesh , typename NamedParameters >
 FT CGAL::Polygon_mesh_processing::face_border_length ( typename boost::graph_traits< PolygonMesh >::halfedge_descriptor h, const PolygonMesh & pmesh, const NamedParameters & np )

#include <CGAL/Polygon_mesh_processing/measure.h>

computes the length of the border polyline that contains a given halfedge.

Template Parameters
 PolygonMesh a model of HalfedgeGraph NamedParameters a sequence of Named Parameters
Parameters
 h a halfedge of the border polyline of which the length is computed pmesh the polygon mesh to which h belongs np optional sequence of Named Parameters among the ones listed below
Named Parameters
 vertex_point_map the property map with the points associated to the vertices of pmesh. If this parameter is omitted, an internal property map for CGAL::vertex_point_t must be available in PolygonMesh geom_traits an instance of a geometric traits class, model of Kernel
Returns
the length of the sequence of border edges of face(h, pmesh). The return type FT is a number type. It is either deduced from the geom_traits Named Parameters if provided, or the geometric traits class deduced from the point property map of pmesh.
Warning
This function involves a square root computation. If Kernel::FT does not have a sqrt() operation, the square root computation will be done approximately.
edge_length()

## ◆ longest_border()

template<typename PolygonMesh , typename NamedParameters >
 std::pair CGAL::Polygon_mesh_processing::longest_border ( const PolygonMesh & pmesh, const NamedParameters & np )

#include <CGAL/Polygon_mesh_processing/measure.h>

finds the longest border of a given triangulated surface and returns a halfedge that is part of this border and the length of this border.

Template Parameters
 PolygonMesh a model of HalfedgeGraph NamedParameters a sequence of Named Parameters
Parameters
 pmesh the polygon mesh np optional sequence of Named Parameters among the ones listed below
Named Parameters
 vertex_point_map the property map with the points associated to the vertices of pmesh. If this parameter is omitted, an internal property map for CGAL::vertex_point_t must be available in PolygonMesh geom_traits an instance of a geometric traits class, model of Kernel
Returns
a pair composed of two members:
• first: a halfedge on the longest border. The return type halfedge_descriptor is a halfedge descriptor. It is deduced from the graph traits corresponding to the type PolygonMesh.
• second: the length of the longest border The return type FT is a number type. It is either deduced from the geom_traits Named Parameters if provided, or the geometric traits class deduced from the point property map of pmesh

## ◆ volume()

template<typename TriangleMesh , typename NamedParameters >
 FT CGAL::Polygon_mesh_processing::volume ( const TriangleMesh & tmesh, const NamedParameters & np )

#include <CGAL/Polygon_mesh_processing/measure.h>

computes the volume of the domain bounded by a closed triangulated surface mesh.

Template Parameters
 TriangleMesh a model of HalfedgeGraph NamedParameters a sequence of Named Parameters
Parameters
 tmesh the closed triangulated surface mesh bounding the volume np optional sequence of Named Parameters among the ones listed below
Precondition
tmesh is closed
Named Parameters
 vertex_point_map the property map with the points associated to the vertices of pmesh. If this parameter is omitted, an internal property map for CGAL::vertex_point_t must be available in TriangleMesh geom_traits an instance of a geometric traits class, model of Kernel
Returns
the volume bounded by tmesh. The return type FT is a number type. It is either deduced from the geom_traits Named Parameters if provided, or the geometric traits class deduced from the point property map of tmesh.